Journal of Nonlinear Mathematical Physics

Articles in Press

Research Article

Compatible Poisson Structures and bi-Hamiltonian Systems Related to Low-dimensional Lie Algebras

Gh. Haghighatdoost, S. Abdolhadi-Zangakani, J. Abedi-Fardad
In Press, Corrected Proof, Available Online: 17 December 2020
In this work, we give a method to construct compatible Poisson structures on Lie groups by means of structure constants of their Lie algebras and some vector field. In this way we calculate some compatible Poisson structures on low-dimensional Lie groups. Then, using a theorem by Magri and Morosi, we...
Research Article

Symmetries of Kolmogorov Backward Equation

Roman Kozlov
In Press, Corrected Proof, Available Online: 10 December 2020
The note provides the relation between symmetries and first integrals of Itô stochastic differential equations and symmetries of the associated Kolmogorov Backward Equation (KBE). Relation between the symmetries of the KBE and the symmetries of the Kolmogorov forward equation is also given.
Research Article

Exact Solutions of a Nonlinear Diffusion Equation with Absorption and Production

Robert Conte
In Press, Corrected Proof, Available Online: 10 December 2020
We provide closed form solutions for an equation which describes the transport of turbulent kinetic energy in the framework of a turbulence model with a single equation.
Research Article

On Ramsey Dynamical Model and Closed-Form Solutions

Gülden Gün Polat, Teoman Özer
In Press, Corrected Proof, Available Online: 21 January 2021
This study focuses on the analysis of Ramsey dynamical model with current Hamiltonian defining an optimal control problem in a neoclassical growth model by utilizing Lie group theory. Lie point symmetries of coupled nonlinear first-order ordinary differential equations corresponding to first-order conditions...
Research Article

Orbits and Lagrangian Symmetries on the Phase Space

Javier Pérez Álvare
In Press, Corrected Proof, Available Online: 12 December 2020
In this article, given a regular Lagrangian system L on the phase space TM of the configuration manifold M and a 1-parameter group G of transformations of M whose lifting to TM preserve the canonical symplectic dynamics associated to L, we determine conditions so that its infinitesimal generator produces...
Research Article

Affine Ricci Solitons of Three-Dimensional Lorentzian Lie Groups

Yong Wang
In Press, Corrected Proof, Available Online: 15 February 2021
In this paper, we classify affine Ricci solitons associated to canonical connections and Kobayashi-Nomizu connections and perturbed canonical connections and perturbed Kobayashi-Nomizu connections on three-dimensional Lorentzian Lie groups with some product structure.
Research Article

On Lie Symmetry Analysis of Certain Coupled Fractional Ordinary Differential Equations

K. Sethukumarasamy, P. Vijayaraju, P. Prakash
In Press, Corrected Proof, Available Online: 31 March 2021
In this article, we explain how to extend the Lie symmetry analysis method for n-coupled system of fractional ordinary differential equations in the sense of Riemann-Liouville fractional derivative. Also, we systematically investigated how to derive Lie point symmetries of scalar and coupled fractional...
Research Article

The Orthogonal and Symplectic Schur Functions, Vertex Operators and Integrable Hierarchies

Linjie Shi, Na Wang, Minru Chen
In Press, Corrected Proof, Available Online: 7 April 2021
In this paper, we first construct an integrable system whose solutions include the orthogonal Schur functions and the symplectic Schur functions. We find that the orthogonal Schur functions and the symplectic Schur functions can be obtained by one kind of Boson-Fermion correspondence which is slightly...
Research Article

Lie Symmetries of the Canonical Connection: Codimension One Abelian Nilradical Case

Hassan Almusawa, Ryad Ghanam, Gerard Thompson
In Press, Corrected Proof, Available Online: 10 April 2021
This paper studies the canonical symmetric connection ∇ associated to any Lie group G. The salient properties of ∇ are stated and proved. The Lie symmetries of the geodesic system of a general linear connection are formulated. The results are then applied to ∇ in the special case where the Lie algebra...
Research Article

A New Case of Separability in a Quartic Hénon-Heiles System

Nicola Sottocornola
In Press, Corrected Proof, Available Online: 25 April 2021
There are four quartic integrable Hénon-Heiles systems. Only one of them has been separated in the generic form while the other three have been solved only for particular values of the constants. We consider two of them, related by a canonical transformation, and we give their separation coordinates...
Research Article

Statistical de Rham Hodge Operators and the Kastler-Kalau-Walze Type Theorem for Manifolds With Boundary

Sining Wei, Yong Wang
In Press, Corrected Proof, Available Online: 29 April 2021
In this paper, we give the Lichnerowicz type formulas for statistical de Rham Hodge operators. Moreover, Kastler-Kalau-Walze type theorems for statistical de Rham Hodge operators on compact manifolds with (respectively without) boundary are proved.
Research Article

A Local Equivariant Index Theorem for Sub-Signature Operators

Kaihua Bao, Jian Wang, Yong Wang
In Press, Corrected Proof, Available Online: 6 May 2021
In this paper, we prove a local equivariant index theorem for sub-signature operators which generalizes Weiping Zhang’s index theorem for sub-signature operators.